Lie symmetries and differential Galois groups of linear equations

Oudshoorn, W.; van der Put, M.

doi:10.1090/S0025-5718-01-01397-7

Lie symmetries and differential Galois groups of linear equations
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by W. R. Oudshoorn and M. van der Put;

Math. Comp. 71 (2002), 349-361

DOI: https://doi.org/10.1090/S0025-5718-01-01397-7

Published electronically: October 4, 2001

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Abstract:

For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In connection with this a new algorithm for computing the Lie symmetries of a linear ordinary differential equation is presented.

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